量子B代数上的正规(正则)同余  

Normal(regular)Congruences on Quantum B-algebras

作　　者：潘芳芳 韩胜伟[2] PAN Fang-fang;HAN Sheng-wei(School of Science,Xi'an University of Posts and Telecommunications,Xi'an 710121,China;School of Mathematics and Stastics,Shanxi Normal University,Xi'an 710119,China)

机构地区：[1]西安邮电大学理学院,陕西西安7100121 [2]陕西师范大学数学与统计学院,陕西西安710119

出　　处：《模糊系统与数学》2024年第3期45-51,共7页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金项目(11971286,12471436)。

摘　　要：量子B代数是Quantale的蕴涵约简形式,它为非可换可代数化逻辑提供了统一的语义。对于量子B代数上的同余,它所对应的商未必是一个量子B代数。本文主要介绍了量子B代数上一类特殊的同余-正规(正则)同余,它所对应的商是一个量子B代数。证明了MV量子B代数上的每一个同余都是正则同余。Quantum B-algebras can be seen as implicational subreducts of quantales,which provide a unified semantics for non-commutative algebraic logic.For a congruence on a quan-tum B-algebra,its corresponding quotient is not necessary a quantum B-algebra.The main work of this paper is to introduce a class of congruences,called normal congruences(regular congruences),such that its corresponding quotient is again a quantum B-algebra.Finally,we prove that every congruence on MV-quantum B-algebras is regular.

关 键 词：量子B代数 QUANTALE 正规同余 正则同余 

分 类 号：O153.1[理学—数学]